Missy is constructing a fence that consists of parallel sides line ab and line ef. complete the proof to explain how she can show that m∠akl = 116° by filling in the missing justifications. statement justification line ab ∥ line ef m∠klf = 116° given m∠klf+ m∠bkl = 180° 1. m∠bkl + m∠akl = 180° linear pair postulate m∠klf + m∠bkl = m∠bkl + m∠akl 2. m∠klf = m∠akl subtraction property m∠akl = m∠klf symmetric property m∠akl = 116° substitution property 1. alternate interior angles theorem; 2. substitution property 1. definition of complementary angles; 2. substitution property 1. definition of supplementary angles; 2. transitive property 1. same-side interior angles theorem; 2. transitive property

1. Definition of Supplementary Angles; 2. Transitive Property

Step-by-step explanation:

Statement Justification:

line AB ∥ line EF  ⇒ (Given)

m∠KLF = 116°       ⇒ (Given)

m∠KLF+ m∠BKL = 180° ⇒ 1. (Definition of Supplementary Angles)

Definition of Supplementary angles is:

"If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees."

m∠BKL + m∠AKL = 180°  ⇒ (Linear Pair Postulate)

m∠KLF + m∠BKL = m∠BKL + m∠AKL ⇒ 2. (Transitive Property)

the transitive property states that:

"If a = b and b = c, then a = c. In other words, if a is related to b by some property, and b is related to c by the same property, then a is related to c by that property."

m∠KLF = m∠AKL   ⇒ (Subtraction Property)

m∠AKL = m∠KLF   ⇒ (Symmetric Property)

m∠AKL = 116°         ⇒ (Substitution Property)

Hence the Final Answer is:

1. Definition of Supplementary Angles; 2. Transitive Property

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step-by-step explanation:

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